For what value of a the quadratic ax^2 +(2a-1)x +a+4 is always positive

Answers (1)

Solution:  We have  ,  ax^2+(2a-1)x+(a+4)

        \ \ Rightarrow hspace1cmD> 0hspace0.5cm and hspace0.5cma> 0\ \ Rightarrow hspace1cmD=(2a-1)^2-4a(a+4)< 0\ \ Rightarrow hspace1cm-8a+1< 0Rightarrow a> frac18\ \ Rightarrow hspace1cmain (frac18,infty)

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